The longer leg of a right triangle is 7 cm more than the shorter leg. The length of the hypotenuse is 3 cm more than twice the length of the shorter leg. Find the length of the hypotenuse.

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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The proportion of samples that will have means between 115 and 120 is 0.4772 or 47.72%.

To solve this problem, we need to use the Central Limit Theorem, which states that the sample means of a large sample size (n>30) from any population with a finite mean and variance will be approximately normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ/sqrt(n)).

Here, the population mean (μ) = 120, and the population standard deviation (σ) = 10. We are given that the sample size (n) = 16, and we need to find the proportion of samples that will have means between 115 and 120.

First, we need to standardize the sample means using the z-score formula:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean.

For the lower limit of 115:

z1 = (115 - 120) / (10 / sqrt(16)) = -2

For the upper limit of 120:

z2 = (120 - 120) / (10 / sqrt(16)) = 0

We need to find the area under the standard normal distribution curve between z1 = -2 and z2 = 0. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we find that the area between z1 = -2 and z2 = 0 is 0.4772.

Therefore, the proportion of samples that will have means between 115 and 120 is 0.4772 or 47.72%.

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The proportion of samples that will have means between 115 and 120 is 0.4772 or 47.72%.

To solve this problem, we need to use the Central Limit Theorem, which states that the sample means of a large sample size (n>30) from any population with a finite mean and variance will be approximately normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ/sqrt(n)).

Here, the population mean (μ) = 120, and the population standard deviation (σ) = 10. We are given that the sample size (n) = 16, and we need to find the proportion of samples that will have means between 115 and 120.

First, we need to standardize the sample means using the z-score formula:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean.

For the lower limit of 115:

z1 = (115 - 120) / (10 / sqrt(16)) = -2

For the upper limit of 120:

z2 = (120 - 120) / (10 / sqrt(16)) = 0

We need to find the area under the standard normal distribution curve between z1 = -2 and z2 = 0. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we find that the area between z1 = -2 and z2 = 0 is 0.4772.

Therefore, the proportion of samples that will have means between 115 and 120 is 0.4772 or 47.72%.

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Solution:

We know that:

\(Original \ price = \$11\)

\(Sale \ price = \$9.25\)

\(\frac{9.25}{11} + \frac{1.75}{11} =100\%\)

Simplify the equation to find the percent off:

\(\frac{9.25}{11} + \frac{1.75}{11} =100\%\)

\(84\% + \bold{16\%} = 100\% \space\ \space\ \space\ \ \ \ \ [Rounded]\)

This means that the original price has decreased about 16%.

The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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Answer:

efefe

Step-by-step explanation:

fef greht jy7i8

Answer:

One

Step-by-step explanation:

5% = .05

20x.05 =

1

:)

Answer:

5% of 20 = 1

Step-by-step explanation:

Step 1: Our output value is 20.

Step 2: We represent the unknown value with x.

Step 3: From step 1 above, 20=100%.

Step 4: Similarly, x=5%.

Step 5: This results in a pair of simple equations:

20=100%(1).

x=5%(2).

Step 6: By dividing equation 1 by equation 2 and noting that both the right hand side of both equations have the same unit (%); we have

20/x = 100%/5%

Step 7: Again, the reciprocal of both sides gives

x/20 = 5/100 ---> 1

Therefore, 5% of 20 is 1.

Answer:

i can't find the answer

Step-by-step explanation:

Answer:

2.7027027027027027

Step-by-step explanation:

1,000 grams make a kilogram

A quadratic function in standard form that passes through the points (-8,0), (-5,-3), and (-2,0) is equals to the f(x) = (1/3)( x² + 10x + 16).

A quadratic function is a polynomial function with one or more variables, the highest degree of the variable is two. It is also called the polynomial of degree 2. The form of quadratic function is

f(x) = ax² + bx + c ----(1)

is determined by three points and must be a≠ 0. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs (-8,0), (-5,-3), and (-2,0) and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point ( -8,0), x = -8, y = f(x) = 0 in equation (1),

=> 0 = a(-8)² + b(-8) + c

=> 64a - 8b + c = 0 --(2)

Similarly, for second point ( -5,-3) , f(x) = -3, x = -5

=> - 3 = a(-5)² + (-5)b + c

=> 25a - 5b + c = -3 --(3)

Continue for third point (-2,0)

=> 0 = a(-2)² + b(-2) + c

=> 4a -2b + c = 0 --(4)

So, we have three equations and three values to determine.

Subtract equation (4) from (2)

=> 64 a - 8b + c - 4a + 2b -c = 0

=> 60a - 6b = 0

=> 10a - b = 0 --(5)

subtract equation (4) from (3)

=> 21a - 3b = -3 --(6)

from equation (4) and (5),

=> 3( 10a - b) - 21a + 3b = -(- 3)

=> 30a - 3b - 21a + 3b = 3

=> 9a = 3

=> a = 1/3

from (5) , b = 10a = 10/3

from (4), c = 2b - 4a = 20/3 - 4/3 = 16/3

So, f(x)= (1/3)( x² + 10x + 16)

Hence, required values are 1/3, 10/3, and 16/3.

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The equation of the perpendicular line is y = 4/3x  - 13

The equation is given as

y = -¾ x - 14

Make y the subject

y = -¾x - 14

The point is also given as

Point = (0, 13)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = -3/4

This means that the slope of y = -¾x - 14  is -3/4

So, we have

m = -3/4

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is 4/3

The equation of the perpendicular lines is then calculated as

y = m(x - x₁) +y₁

Where

m = 4/3

(x₁, y₁) = (0, 13)

So, we have

y = 4/3(x + 0) - 13

Evaluate

y = 4/3x  - 13

Hence, the perpendicular line has an equation of y = 4/3x  - 13

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The centroid of the triangle with vertices (-1, 0), (1, 0), and (0, 13) is (0, 4).

To find the centroid, we calculate the average of the coordinates of the vertices. The x-coordinate of the centroid is the average of the x-coordinates of the vertices, which is (-1 + 1 + 0)/3 = 0. The y-coordinate of the centroid is the average of the y-coordinates of the vertices, which is (0 + 0 + 13)/3 = 13/3 = 4 1/3 = 4 (approximately).

The centroid of a triangle is the point of intersection of its medians, and each median divides the triangle into two smaller triangles with equal areas. The median from a vertex of the triangle passes through the midpoint of the opposite side. Since the medians divide each side in a 1:2 ratio, the centroid is located one-third of the way from each side toward the opposite vertex. Thus, the centroid of this triangle is located at (0, 4).

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The length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Let L be the length and W be the width of the rectangle.

From the question:

L = 420 + W (based on the data given in the question)

LW  = 13

(420 + W)W = 13

W² + 420W - 13 = 0

After solving the above quadratic equation:

W = 0.031, W = -420.03 (width cannot be negative)

W = 0.031 yards (which is not practical but from a mathematical point of view it can be considered)

L = 420 + 0.031 = 420.031 yards

Thus, the length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

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Answer:

well, I think b would be correct if we use the cosine rule but according to my calculations a is the answer when we use sin rule but I'm not really sure.

Answer:

x = 2/3

0r 0.6(6)

both are positive

Step-by-step explanation:

3x - 5 = -3 is the answer positive or negative?

3x - 5 = -3

3x = -3 + 5

3x = 2

x = 2/3

0r 0.6(6)

The sum of interior angles of the given polygon is 900 degrees

The formula used to calculate the sum of an interior angle of a polygon is expressed as:

Sum of interior angles = ( n − 2 ) × 180 ∘

n is the number of sides

The number of sides of the given polygon is 7, hence;

Sum of interior angles = (7 − 2 ) × 180 ∘

Sum of interior angles = 5 ×  180 ∘

Sum of interior angles = 900 degrees

Hence the sum of interior angles of the given polygon is 900 degrees

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There are 8 capsules should be given to patient.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

A patient is to receive 2.6 grams of medication.

And, The medication is available in capsules of 325 milligrams.

Here, We know that;

1 gram = 1,000 milligrams

⇒ 2.6 grams = 2.6 × 1000

                    = 2,600 milligrams

Hence, Number of capsules = 2600/325

                                            = 8

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Answer:

60 minutes

Step-by-step explanation:

Latitude and longitude are measuring lines used for locating places on the surface of the Earth. They are angular measurements, expressed as degrees of a circle. A full circle contains 360°. Each degree can be divided into 60 minutes, and each minute is divided into 60 seconds.

One degree of latitude is equal to approximately 60 nautical miles or 69 statute miles. Since a minute of latitude is one-sixtieth of a degree, it follows that one degree of latitude is equal to 60 minutes.

This means that there are 60 nautical miles or 69 statute miles between two points that differ by one minute of latitude.

The minute of latitude is a widely used unit for measuring distances on Earth, particularly in navigation and aviation. It allows for precise calculations and is crucial for determining positions accurately. Understanding the relationship between degrees of latitude and minutes helps in determining distances, estimating travel times, and ensuring accurate navigation across the globe.

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The calculated measure of the angle B is 12 degrees

From the question, we have the following parameters that can be used in our computation:

Using the sum of opposite interior angles, we have

C  = A + B

Substitute the known values in the above equation, so, we have the following representation

6x + 9 + x - 8 = 141

When the like terms are evaluated, we have

7x + 1 141

So, we have

7x = 140

Divide

x = 20

This means that

m∠B=(x − 8)∘

Substitute the known values in the above equation, so, we have the following representation

m∠B=(20 − 8)∘

Evaluate

m∠B = 12∘

Hence, the measure of the angle is 12 degrees

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Using Composition of functions, the value of g(h(24)) = 1158.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

The new function h is created by combining the two functions f and g, where h(x) = f(g(x)) for all x in g's domain where g(x) is in f's domain. Function composition is denoted by the notation h = f • g, also written as h(x) = (f • g)(x), which can be interpreted as "f of g of x."

Given,

g(x) = 2x + 4, h(x) = x² +1

Using composition of functions,

⇒ h(24) = 24² + 1

⇒ g(h(24)) = 2 (24² + 1) + 4

⇒ g(h(24)) = 2 × 577 + 4

⇒ g(h(24)) = 1158

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Answer:

x + y = -6

Step-by-step explanation:

Just put x and y and add the number on the RHS
Its really not that hard

But i hope it helped

Answer:

8 goody bags

Step-by-step explanation:

Answer:

\( = - 7 {n}^{2} - 49 + 8 {n}^{3} + 56n \\ = - 7( {n}^{2} + 7) + 8n( {n}^{2} + 7) \\ = \boxed{ ( {n}^{2} + 7)(8n -7 )}\)

Making "a" the subject of the formula would give us: a = 8 - b - c/2

Given the formula, 8 = a+b+c/2, to make a the subject of the formula, we would isolate a in the equation.

8 = a+b+c/2

8 = (2a + 2b + c)/2

2(8) = 2a + 2b + c

16 = 2a + 2b + c

16 - 2b - c = 2a

Divide both sides by 2

16/2 - 2b/2 - c/2 = 2a/2

8 - b - c/2 = a

a = 8 - b - c/2

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When \($a < 1$\)\($\delta=-1 \pm j \sqrt{2 a} \rightarrow$\) Here two solutions oscillate when a is negative, the system has repeated eigen value when \($a=0$\), when \($a=0$\\\), then both solutions decay exponentially without oscillating,

The given Vector equation, When a is negative real number then both solutions grow exponentially with system oscillating.

\($$\left.\begin{array}{l}y^{\prime}=\text { Ay } \\A=\left(\begin{array}{cc}-1 & a \\2 & -1\end{array}\right)\end{array}\right\}\)

Now we will solve 2-

           \($$|A-\delta I|=\left|\begin{array}{cc}-1-\lambda & a \\2 & -1-\lambda\end{array}\right|=0$$\)

Now multiply, we get.

\($$\begin{aligned}& (-1-\lambda)(-1-\lambda)-2 a=0 \\& 1+2 \lambda^2-2 a=0 \\& s^2+2 \lambda+1-2 a=0 \text { (1) }\end{aligned}$$\)

Now we will find both 2 values of d.

\($\left(\begin{array}{c}\text { if } a x^2+b x+c=0 \\ d=\frac{-2 \pm \sqrt{(2)^2-(4)(1)(1-2 a)}}{2(1)} \leftarrow\left(x=\frac{-b \pm \sqrt{b^2-4-a c}}{2 a}\right.\end{array}\right)$$$\)

\(& =-1 \pm \frac{1}{2} \sqrt{4-4+8 a} \\\lambda & =-1 \pm \sqrt{2 a} .\end{aligned}$$\)

(a) when \($a < 1$\)\($\delta=-1 \pm j \sqrt{2 a} \rightarrow$\) Here two solutions oscillate when a is negative.

(b) put \($a=0$\)

\($$\begin{aligned}& d=-1 \pm \sqrt{2 a} \\& d=-1 \pm \sqrt{2 \times 0} \\& d=-1 \pm 0 \\& r=-1\end{aligned}$$\)

mean \($s_1=\sqrt{2}_2=-1$\), here system has repeated eigen value when \($a=0$\)

(c) when \($a=0$\\\), then both solutions decay exponentially without oscillating.

(d) Now, when use put \($a=2$.\)

\($$\begin{aligned}& \delta=-1 \pm \sqrt{2 a} \\& \text { when } \\& a=2 \\& \delta=-1 \pm \sqrt{2 \times 2} \\& s_1=-1 \pm 2 \\& \delta_1=1\end{aligned}$$\)

In the one of the solution decay exponentially and the other Grow exponentially.

(e). When a is negative real number then both solutions grow exponentially with system oscillating.

Therefore,When \($a < 1$\)\($\delta=-1 \pm j \sqrt{2 a} \rightarrow$\) Here two solutions oscillate when a is negative, the system has repeated eigen value when \($a=0$\), when \($a=0$\\\), then both solutions decay exponentially without oscillating,

The given Vector equation, When a is negative real number then both solutions grow exponentially with system oscillating.

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We need to check if 13 divides (20192018 - (1-1)") + 4H0. By performing the calculations, we find that 13 does not divide (20192018 - (1-1)") + 4H0. Hence, 20192018 is not divisible by 13.

To prove that 13 divides a number "a" if and only if 13 divides (an - (1-1)") + 4H0, we need to show that both conditions imply each other
First, let's assume that 13 divides "a". This means that "a" can be written as 13k, where k is an integer. We can express this in terms of base 10 as (13k - (1-1)") + 4H0. Simplifying further, we get (13k - 1) + 4H0. Since 13 divides 13k and 13 divides 4H0, it also divides their sum. Therefore, if 13 divides "a", it also divides (an - (1-1)") + 4H0.
Next, let's assume that 13 divides (an - (1-1)") + 4H0. This means that (an - (1-1)") + 4H0 can be written as 13k, where k is an integer. Simplifying the expression, we get an - (1-1)") + 4H0 = 13k. Rearranging, we have an = 13k + (1-1)") + 4H0. Since 13 divides 13k + (1-1)") + 4H0, it also divides their sum. Therefore, if 13 divides (an - (1-1)") + 4H0, it also divides "a".
In conclusion, we have proven that 13 divides "a" if and only if 13 divides (an - (1-1)") + 4H0.
To decide whether 20192018 is divisible by 13, we can apply the result from part (a). Let's express 20192018 as (an - (1-1)") + 4H0. Since 13 divides (an - (1-1)") + 4H0, if 13 divides 20192018, it will also divide (an - (1-1)") + 4H0. Therefore, we need to check if 13 divides (20192018 - (1-1)") + 4H0. By performing the calculations, we find that 13 does not divide (20192018 - (1-1)") + 4H0. Hence, 20192018 is not divisible by 13.

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Answer:

110 hope u get a good grade:) add me on ig welia.martinez

.

Step-by-step explanation:

Answer:

The solution to the recurrence relation is given by an = 2^(n+1) - 1.

Step-by-step explanation:

(a) To solve the recurrence relation an = an-2 + 4, with initial conditions a1 = 3 and a2 = 5, we'll consider two cases: one for when n is even and one for when n is odd.

For n even:

Substituting n = 2k (where k is a positive integer) into the recurrence relation, we get:

a2k = a2k-2 + 4

Now let's write out a few terms to observe the pattern:

a2 = a0 + 4

a4 = a2 + 4

a6 = a4 + 4

...

We notice that a2k = a0 + 4k for even values of k.

Using the initial condition a2 = 5, we can find a0:

a2 = a0 + 4(1)

5 = a0 + 4

a0 = 1

Therefore, for even values of n, the solution is given by an = 1 + 4k.

For n odd:

Substituting n = 2k + 1 (where k is a non-negative integer) into the recurrence relation, we get:

a2k+1 = a2k-1 + 4

Again, let's write out a few terms to observe the pattern:

a3 = a1 + 4

a5 = a3 + 4

a7 = a5 + 4

...

We see that a2k+1 = a1 + 4k for odd values of k.

Using the initial condition a1 = 3, we find:

a3 = a1 + 4(1)

a3 = 3 + 4

a3 = 7

Therefore, for odd values of n, the solution is given by an = 3 + 4k.

(b) To solve the recurrence relation an = 2an-1 + 1, with initial condition a1 = 1, we'll find a general expression for an.

Let's write out a few terms to observe the pattern:

a2 = 2a1 + 1

a3 = 2a2 + 1

a4 = 2a3 + 1

...

We can see that each term is one more than twice the previous term.

By substituting repeatedly, we can express an in terms of a1:

an = 2(2(2(...2(a1) + 1)...)) + 1

= 2^n * a1 + (2^n - 1)

Using the initial condition a1 = 1, we have:

an = 2^n * 1 + (2^n - 1)

= 2^n + 2^n - 1

= 2 * 2^n - 1

Therefore, the solution to the recurrence relation is given by an = 2^(n+1) - 1.

Answer:

final price:56.56

tax amount:3.39

9:16

area =scale factor squared